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3. Use Maxwell relations to determine an expression for the change in entropy of a van der Waals gas with respect to a change in volume.

3. Use Maxwell relations to determine an expression for the change in entropy of a van der Waals gas with respect to a change in volume.

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter4: Gibbs Energy And Chemical Potential
Section: Chapter Questions
Problem 4.5E: Prove that the adiabatic free expansion of an ideal gas is spontaneous.
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3. Use Maxwell relations to determine an expression for the change in entropy of a van der Waals gas with respect to a change in volume.
Transcribed Image Text:3. Use Maxwell relations to determine an expression for the change in entropy of a van der Waals gas with respect to a change in volume.
If we ad Equation 22.49, or add d (PV) to Equation 22.50, we get The other equations of this section follow by comparing the total derivative of each function in terms of its natural variables to the above equations for dU, dH, dA, and dG. Table 22.1 summarizes some of the principal equations we have derived in this and previous chapters. Thermodynamic energy U TABLE 22.1 are The four principal thermodynamic energies, their differential expressions, and the corresponding Maxwell relations. d(TS) from Equation 22.48, or subtract d(TS) from Н H____ noileupiti moit ban onsup og airt To A dG = -SdT + VdP G Differential expression dU = TdS - PdV priboo 101 zi pal dH = TdS+ VdP 1151 dA==SdT - PdV dG = -SdT + VdP Corresponding Maxwell relations (7),=-(-35), as S av (F).-(53). S Ꮪ (as), T a P as ab 5/5 V P 10 Vas as (P), --(57), T (22.51) P 22-6. The Standard State for a Gas at Any Temperature Is the Hypothetical Ideal Gas at One Bar V (a) die lud ang fashi ant the One of the most important applications of Equation 22.33 involves the correction for nonideality that we make to obtain the standard molar entropies of gases. The hypothetical ideal gas at one bar and at the same temperature. This correction is usually standard molar entropies of gases tabulated in the literature are expressed in terms of a small and is obtained in the following two-step procedure (Figure 22.6). We first take bar to some very low pressure Pid, where it is sure our real
Transcribed Image Text:If we ad Equation 22.49, or add d (PV) to Equation 22.50, we get The other equations of this section follow by comparing the total derivative of each function in terms of its natural variables to the above equations for dU, dH, dA, and dG. Table 22.1 summarizes some of the principal equations we have derived in this and previous chapters. Thermodynamic energy U TABLE 22.1 are The four principal thermodynamic energies, their differential expressions, and the corresponding Maxwell relations. d(TS) from Equation 22.48, or subtract d(TS) from Н H____ noileupiti moit ban onsup og airt To A dG = -SdT + VdP G Differential expression dU = TdS - PdV priboo 101 zi pal dH = TdS+ VdP 1151 dA==SdT - PdV dG = -SdT + VdP Corresponding Maxwell relations (7),=-(-35), as S av (F).-(53). S Ꮪ (as), T a P as ab 5/5 V P 10 Vas as (P), --(57), T (22.51) P 22-6. The Standard State for a Gas at Any Temperature Is the Hypothetical Ideal Gas at One Bar V (a) die lud ang fashi ant the One of the most important applications of Equation 22.33 involves the correction for nonideality that we make to obtain the standard molar entropies of gases. The hypothetical ideal gas at one bar and at the same temperature. This correction is usually standard molar entropies of gases tabulated in the literature are expressed in terms of a small and is obtained in the following two-step procedure (Figure 22.6). We first take bar to some very low pressure Pid, where it is sure our real
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ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
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